If it were "offer", for example, then the sentence would be, "Some governments even offer directly to help protect etc."
So you mean that the word order in the sentence determines the modified element?
In that specific case, yes: the location of the adverb in the sentence clarifies which of the verbs it's modifying.
Is it wrong that we can adverbs anywhere in sentences?
Unfortunately English is my native language, I never studied English grammar as a subject, so I'm unable to identify a general rule.
Saying you could use it literally "anywhere" in sentences would a bit too liberal.
I'd suggest the best ways (perhaps the only correct ways) to use it would be as follows:
To modify "offer":
a. Some governments even offer directly to help protect etc.
b. Some governments even directly offer to help protect etc.
To modify "help":
a. Some governments even offer to directly help protect etc.
b. Some governments even offer to help directly to protect etc. (<-- note the added "to")
To modify "protect":
a. Some governments even offer to help protect their critical infrastructure directly
b. Some governments even offer to help directly protect their critical infrastructure
Note the difference between 2b and 3b.
And 2a is modifying "help protect".